# Cardinal number Sentence Examples

cardinal number
• Two classes between which a one-one relation exists have the same cardinal number and are called cardinally similar; and the cardinal number of the class a is a certain class whose members are themselves classes - namely, it is the class composed of all those classes for which a one-one correlation with a exists.

• Thus the cardinal number of a is itself a class, and furthermore a is a member of it.

• Thus the cardinal number one is the class of unit classes, the cardinal number two is the class of doublets, and so on.

• The cardinal number zero is the class of classes with no members; but there is only one such class, namely - the null class.

• Zero is a cardinal number.

• If a is a cardinal number, a+I is a cardinal number.

• The relation-number of a relation should be compared with the cardinal number of a class.

• Now if n be any finite cardinal number, it can be proved that the class of those serial relations, which have a field whose cardinal number is n, is a relation-number.

• The definition of the ordinal number requires some little ingenuity owing to the fact that no serial relation can have a field whose cardinal number is 1; but we must omit here the explanation of the process.

• But the definition of the cardinal number of a class applies when the class is not finite, and it can be proved that there are different infinite cardinal numbers, and that there is a least infinite cardinal, now usually denoted by o where to is the Hebrew letter aleph.